|
|
A068019
|
|
Composite n such that both 1 + phi(n) and -1 + phi(n) are primes, i.e., phi(n) is the middle term between twin primes (A014574).
|
|
4
|
|
|
8, 9, 10, 12, 14, 18, 21, 26, 27, 28, 36, 38, 42, 49, 54, 62, 77, 86, 91, 93, 95, 98, 99, 111, 117, 122, 124, 133, 135, 146, 148, 152, 154, 171, 182, 186, 189, 190, 198, 206, 209, 216, 217, 218, 221, 222, 228, 234, 252, 266, 270, 278, 279, 287, 291, 297, 302
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
|
|
LINKS
|
|
|
EXAMPLE
|
n = 21, 26, 28, 36, 42 give phi(n)=12; the corresponding twin primes are {11,13}.
|
|
MATHEMATICA
|
Do[s=-1+EulerPhi[n]; s1=1+EulerPhi[n]; If[PrimeQ[s]&&PrimeQ[s1]&&!PrimeQ[n], Print[n]], {n, 1, 2000}]
(* Second program: *)
Select[Range[4, 302], And[CompositeQ@ #, AllTrue[EulerPhi@ # + {-1, 1}, PrimeQ]] &] (* Michael De Vlieger, Dec 08 2018 *)
|
|
PROG
|
(PARI) isok(n) = !isprime(n) && isprime(eulerphi(n)+1) && isprime(eulerphi(n)-1); \\ Michel Marcus, Dec 08 2018
(GAP) Filtered([1..310], n->not IsPrime(n) and IsPrime(1+Phi(n)) and IsPrime(-1+Phi(n))); # Muniru A Asiru, Dec 08 2018
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|